Dominic Harion & Ann Kiefer

“With Big Data and the associated algorithms, we are witnessing an increased return of mathematics and scientific methods to the organisation of social matters”, stated Felix Stalder on automated decision systems in our digital cultures (Stalder, 2017). Far from the importance bestowed upon them in computer science, algorithms are, firstly, in general terms, “a set of instructions for solving a problem or a type of problems and are made up of a finite number of well-defined units”. Even instructions for use of a machine and recipes are ultimately just algorithms. Understanding what such algorithmicity means in our world and what it entails particularly when it is interlaced with the technology we use in our day-to-day lives, plays a role in a well-founded educational requirement, as do the skills to model, apply and modify it, if necessary. First of all, algorithms are neither specifically technological, technical nor even computational. However, they can no longer (and should not) be removed from our infrastructures. In these specific forms, they are responsible for complex processes.

When it comes to the systems of mapping and transport management in topography, algorithms play an integral part in social organisation processes. Public transport maps and transport applications are two specific examples of this. “The shortest path  algorithm” on a graph, also known in specialist settings as the Breadth-first search algorithm or Dijkstra’s algorithm (in cases where the graph’s nodes have weighs) represents a case study similar to everyday life and, at the same time, it can be easily studied independently for use in class. As part of the module presented herein, a fun and collaborative approach was chosen using Involution©, a mathematical game or puzzle developed at the University of Luxembourg by Hugo Parlier and Bruno Teheux. Learning about algorithmic modelling using fun and competitive steps has been tried and discussed for a long time with the help of the Rubik’s Cube (see, for example, Lakkaraju et al., 2022). It opens up learning pathways to the mathematics and computer science interface (see, for example, Joyner, 2008; Agosinelli et al., 2019). Although these cubes can be used to illustrate 3D models, Involution© allows us to reproduce and clarify algorithmic models in a 2D space. Therefore, this game is ideal for expanding interdisciplinary educational horizons in the computational sciences through the formation of mathematical models linked to real world problems: the solution to Involution© lies in finding the shortest path in an underground train system, a task that the pupils already know from the Digital Sciences course (Digital Sciences, 2021). Children and adolescents from different age groups have already explored the search for the shortest path and it has been used to embody formal abstract models (cf. Gibson, 2012). It can therefore be used with gradual levels of difficulty for differentiated learning.

From a teaching perspective, the module is based on the two principles of problem-based and cooperative learning. A template and basic instructions are given to pupils who are faced with a problem. It encourages pupils to use a targeted cognitive process in order to transform a given situation into a target situation, without providing an obvious method to solve the problem, while, at the same time, appealing to creative and critical thinking (cf. Mayer & Wittrock, 2006). This approach inspires pupils to change their opinion on STEM (Science, Technology, Engineering and Mathematics) subjects. For many young people, these subjects are about finding the “one and only solution” and doing so as quickly as possible, yet that does not reflect the reality of the scientific world. Generally speaking, STEM professionals do not have a clear idea of the direction to take to find a solution. This mindset is sometimes overlooked in STEM subjects at school.

Games and puzzles like Involution© provide the perfect framework to develop pupil resilience. “Resilience is related to students’ affective ability to deal with and be able to overcome obstacles and negative situations in the learning process, turning those negative situations into situations that support them.” (Hutauruk & Priatna, 2017). Pupils who are not used to managing frustrating learning circumstances and failures see them as very negative. However, if pupils become used to it, then this experience of resilience will have extremely positive outcomes for the studies and future employment of young people (Hutauruk & Priatna, 2017).

Each pupil does not solve the task individually, but in pairs or small groups. It is designed to be competitive (but not in the sense of a competition), like a class rally. This fun and motivating approach also encourages pupils to model and articulate their personal solutions and offers opportunities for learning by teaching, as the pupils have to express their thought process and back it up with arguments. A configuration in which the groups are constituted homogenously based on the difficulty of the tasks could be considered, as could another configuration with heterogenous groups in which the pupils are coached by their classmates while they come up with solutions.

References
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